Modeling Non-Gaussian Time-correlated Data Using Nonparametric Bayesian Method
Zhiguang Xu · OhioLink ETD Center (Ohio Library and Information Network) · 2014
This dissertation proposes nonparametric Bayesian methods to study a large class of non-Gaussian time-correlated data, including non-Gaussian time series and non-Gaussian longitudinal datasets.When a time series is noticeably non-Gaussian, classical methods with Gaussian innovations will yield poor fits and forecasts, but the joint distribution of a non-Gaussian time series is often difficult to specify.To overcome this difficulty, we propose the copula-transformed AR (CTAR) model.This model utilizes the copula method to determine the joint distribution of the observed series by separating the marginal distribution from the serial dependence.In implementation, we model the observed series as a nonlinear, nonparametric transformation from a latent Gaussian series.The marginal distribution of the observed series follows a nonparametric Bayesian prior distribution having large support, and therefore any non-Gaussian distribution can be well approximated.The dependence structure of the observed series is characterized indirectly through the latent Gaussian time series, so that we can borrow some classic Gaussian time series modeling methods to model the serial dependence.We also extend the proposed nonparametric Bayesian copula methods to model stationary time series with changing conditional volatility by developing copula-transformed AR-GARCH (CTAR-GARCH) model, which describes the observed series as a nonlinear, nonparametric transformation from an AR-GARCH First and foremost, I would like to express my sincere gratitude to my co-advisors-Dr.MacEachern and Dr. Xu.It is through their detailed guidance that I learned how to conduct research and formulate a well-grounded statistical analysis, and I cannot achieve my research goals without their support.I am grateful to Dr. MacEachern for enlightening me with his thought-provoking ideas and impressing me with his rigorous writing style.I am grateful to Dr. Xu for providing deep insight in discussions and giving me valuable advice in sharpening dissertation writing skills.Also, I would like to express my sincere thanks to Dr. Peruggia